Finite Group Databasebeta

← C11×#32924 #14610117

Subgroups — C11×#32924 #14610117

Order 2816.

1468 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C11×#3040C212yesmaximal, complemented
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C2×C11×#453C211yesmaximal, characteristic
5C11×#2544C211yesmaximal, characteristic, complemented
6C11×#1887C211yesmaximal, characteristic, complemented
7C11×#1885C211yesmaximal, characteristic, complemented
8C11×#1883C212yesmaximal, complemented
9C11×#1882C212yesmaximal, complemented
10C11×#1806C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic, complemented
18C11×#520—22no—
19C11×#520C2212yes—
20C11×#518—22no—
21C11×#518—22no—
22C11×#518C2211yescharacteristic
23C4×C11×#41—22no—
24C4×C11×#41C2212yes—
25C2×C4×D4×C11—22no—
26C2×C4×D4×C11—22no—
27C2×C4×D4×C11C2211yescharacteristic
28C11×#464—22no—
29C11×#464—22no—
30C11×#463—22no—
31C11×#463—22no—
32C11×#455—24no—
33C11×#453—24no—
34C11×#423C2212yescomplemented
35C2×C11×#104C2212yes—
36C2×C11×#104C2212yes—
37C11×#419C2212yescomplemented
38C11×#418C2212yescomplemented
39C2×C11×#100C2211yescharacteristic
40C2×C11×#100C2211yescharacteristic
41C11×#394—22no—
42C11×#391C2211yescharacteristic, complemented
43C11×#390C2211yescharacteristic, complemented
44C11×#386—22no—
45C4×C11×C4⋊C4C2211yescharacteristic, complemented
46C11×#343C2212yescomplemented
47C11×#339C2212yescomplemented
48C11×#339C2212yescomplemented
49C11×H(5,𝔽2)—24no—
50C11×H(5,𝔽2)—22no—
51C11×H(5,𝔽2)D414yes—
52C2×C11×#41—22no—
53C2×C11×#41C2312yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11D412yes—
62C11×#137—24no—
63C11×#137—24no—
64C11×AGL(1,ℤ/8)—24no—
65C11×AGL(1,ℤ/8)—24no—
66C2×C11×Q16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×D8—22no—
70C2×C11×M16C2312yes—
71C2×C11×M16C2312yes—
72C11×#127—22no—
73C11×#127—22no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11D412yescomplemented
80C4×Q8×C11D412yescomplemented
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C4×D4×C11—24no—
84C4×D4×C11—24no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11D412yescomplemented
94C4×D4×C11D412yescomplemented
95C11×#117—24no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117C2312yes—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4D412yes—
111C2×C42×C11—22no—
112C2×C42×C11—22no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×C4⋊C8—22no—
117C11×C4⋊C8—22no—
118C11×#104—24no—
119C11×#104—24no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#100—22no—
125C11×#100—22no—
126C11×#95—21no—
127C11×#95—22no—
128#32924C1111yesmaximal, characteristic, direct product factor, Sylow
129C24×C11—22no—
130C24×C11—21no—
131C24×C11C2×D412yes—
132C11×#41—28no—
133C11×#41—28no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41C2×D414yes—
137C11×#41#4114yes—
138C2×Q8×C11—22no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—24no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11—22no—
148C2×D4×C11—28no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—44no—
156C2×D4×C11—44no—
157C2×D4×C11—82no—
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11#4112yes—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—82no—
174C22×C4×C11—84no—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C11×Q16—44no—
180C11×SD16—44no—
181C11×SD16—44no—
182C11×D8—44no—
183C11×M16—22no—
184C11×M16—22no—
185C11×M16—22no—
186C11×M16—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—44no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—82no—
207C42×C11—24no—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11C2×D412yes—
216C42×C11C2×D412yes—
217C4×H(5,𝔽2)C2×C1111yescharacteristic, complemented
218#3040C2×C1112yescomplemented
219C2×#455C2×C1111yescharacteristic, complemented
220C2×#453C2×C1111yescharacteristic
221#2544C2×C1111yescharacteristic, complemented
222#1887C2×C1111yescharacteristic, complemented
223#1885C2×C1111yescharacteristic, complemented
224#1883C2×C1112yescomplemented
225#1882C2×C1112yescomplemented
226#1806C2×C1112yescomplemented
227#1800C2×C1111yescharacteristic, complemented
228C23×C11—28no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—82no—
240C23×C11—82no—
241C23×C11#12114yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11#12114yes—
247D4×C11—216no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—24no—
251D4×C11—22no—
252D4×C11—24no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—88no—
256D4×C11#12114yes—
257C2×C4×C11—28no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—82no—
279C2×C4×C11—82no—
280C2×C4×C11—82no—
281C2×C4×C11—84no—
282C2×C4×C11—82no—
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12012yes—
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D412yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4111yescharacteristic
290C8×C11—42no—
291C8×C11—42no—
292C2×H(5,𝔽2)C22×C1111yescharacteristic
293C2×#137C22×C1112yes—
294C2×AGL(1,ℤ/8)C22×C1112yes—
295C2×#127C22×C1111yescharacteristic
296C2×#124C22×C1111yescharacteristic
297C2×#124C22×C1111yescharacteristic, complemented
298#520—22no—
299#520C22×C1112yes—
300#518—22no—
301#518—22no—
302#518C22×C1111yescharacteristic
303C4×#41—22no—
304C4×#41C22×C1112yes—
305C2×C4×D4—22no—
306C2×C4×D4—22no—
307C2×C4×D4C22×C1111yescharacteristic
308#464—22no—
309#464—22no—
310#463—22no—
311#463—22no—
312#455—24no—
313#453—24no—
314#423C22×C1112yescomplemented
315C2×#104C22×C1112yes—
316C2×#104C22×C1112yes—
317#419C22×C1112yescomplemented
318#418C22×C1112yescomplemented
319C2×#100C22×C1111yescharacteristic
320C2×#100C22×C1111yescharacteristic
321#394—22no—
322#391C22×C1111yescharacteristic, complemented
323#390C22×C1111yescharacteristic, complemented
324#386—22no—
325C4×C4⋊C4C22×C1111yescharacteristic, complemented
326#343C22×C1112yescomplemented
327#339C22×C1112yescomplemented
328#339C22×C1112yescomplemented
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—24no—
332C22×C11—24no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—88no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11C2×#12011yescharacteristic
346C22×C11C2×#12111yescharacteristic
347C22×C11#52511yescharacteristic
348C4×C11—24no—
349C4×C11—22no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#12112yes—
359C4×C11#52512yes—
360H(5,𝔽2)—24no—
361H(5,𝔽2)—22no—
362H(5,𝔽2)D4×C1114yes—
363C2×#41—22no—
364C2×#41C23×C1112yes—
365C22×Q8C23×C1111yescharacteristic
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4C23×C1111yescharacteristic
370C22×D4C23×C1111yescharacteristic
371C23×C4—22no—
372C23×C4D4×C1112yes—
373#137—24no—
374#137—24no—
375AGL(1,ℤ/8)—24no—
376AGL(1,ℤ/8)—24no—
377C2×Q16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×D8—22no—
381C2×M16C23×C1112yes—
382C2×M16C23×C1112yes—
383#127—22no—
384#127—22no—
385#124—22no—
386#124—22no—
387#124—22no—
388#124—22no—
389C4×Q8—22no—
390C4×Q8D4×C1112yescomplemented
391C4×Q8D4×C1112yescomplemented
392C4×D4—24no—
393C4×D4—24no—
394C4×D4—24no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—24no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4D4×C1112yescomplemented
405C4×D4D4×C1112yescomplemented
406#117—24no—
407#117—22no—
408#117—22no—
409#117C23×C1112yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C23×C1111yescharacteristic
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4D4×C1112yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42C23×C1111yescharacteristic
425C2×C42C23×C1111yescharacteristic
426C2×C42C23×C1111yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429#104—24no—
430#104—24no—
431#103—22no—
432#103—22no—
433#102—22no—
434#102—22no—
435#100—22no—
436#100—22no—
437#95—21no—
438#95—22no—
439C2×C11—21no—
440C2×C11—21no—
441C2×C11—44no—
442C2×C11—44no—
443C2×C11—161no—
444C2×C11#284711yescharacteristic
445C2×C11#301811yescharacteristic
446C2×C11#301911yescharacteristic
447C24—22no—
448C24—21no—
449C24C2×D4×C1112yes—
450#41—28no—
451#41—28no—
452#41—22no—
453#41—22no—
454#41C2×D4×C1114yes—
455#41C11×#4114yes—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8C2×D4×C1112yes—
461C2×D4—24no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—22no—
466C2×D4—28no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—82no—
476C2×D4C2×D4×C1112yes—
477C2×D4C2×D4×C1112yes—
478C2×D4C11×#4112yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—82no—
492C22×C4—84no—
493C22×C4C2×D4×C1112yes—
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C24×C1111yescharacteristic
497Q16—44no—
498SD16—44no—
499SD16—44no—
500D8—44no—
501M16—22no—
502M16—22no—
503M16—22no—
504M16—22no—
505C2×C8—22no—
506C2×C8—22no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—42no—
512C4⋊C4C2×D4×C1112yes—
513C4⋊C4C2×D4×C1112yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—24no—
520C22⋊C4—44no—
521C22⋊C4—41no—
522C22⋊C4—42no—
523C22⋊C4—41no—
524C22⋊C4—82no—
525C42—24no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42C2×D4×C1112yes—
534C42C2×D4×C1112yes—
535C11#3292411yescharacteristic, direct product factor, Sylow
536C23—28no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—82no—
548C23—82no—
549C23C11×#12114yes—
550C23C22×D4×C1111yescharacteristic
551Q8—22no—
552Q8—42no—
553Q8—42no—
554Q8C11×#12114yes—
555D4—216no—
556D4—24no—
557D4—24no—
558D4—24no—
559D4—22no—
560D4—24no—
561D4—42no—
562D4—42no—
563D4—88no—
564D4C11×#12114yes—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—84no—
590C2×C4—82no—
591C2×C4C11×#12011yescharacteristic
592C2×C4C11×#12012yes—
593C2×C4C11×#12011yescharacteristic
594C2×C4C22×D4×C1111yescharacteristic
595C2×C4C22×D4×C1112yes—
596C2×C4C2×C11×#4112yes—
597C2×C4C2×C11×#4111yescharacteristic
598C8—42no—
599C8—42no—
600C22—21no—
601C22—21no—
602C22—24no—
603C22—24no—
604C22—44no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—88no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22C2×C11×#12011yescharacteristic
617C22C2×C11×#12111yescharacteristic
618C22C11×#52511yescharacteristic
619C4—22no—
620C4—21no—
621C4—21no—
622C4—24no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4C2×C11×#12112yes—
630C4C11×#52512yes—
631C2—21no—
632C2—21no—
633C2—44no—
634C2—44no—
635C2—161no—
636C2C11×#284711yescharacteristic
637C2C11×#301811yescharacteristic
638C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#453C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×C11×H(5,𝔽2)C2semidirect
2. C11×#3040C2semidirect
3. C2×C11×#455C2semidirect
5. C11×#2544C2semidirect
6. C11×#1887C2semidirect
7. C11×#1885C2semidirect
8. C11×#1883C2semidirect
9. C11×#1882C2semidirect
10. C11×#1806C2semidirect
11. C11×#1800C2semidirect
17. C2×C11×#124C22semidirect
34. C11×#423C22semidirect
37. C11×#419C22semidirect
38. C11×#418C22semidirect
42. C11×#391C22semidirect
43. C11×#390C22semidirect
45. C4×C11×C4⋊C4C22semidirect
46. C11×#343C22semidirect
47. C11×#339C22semidirect
48. C11×#339C22semidirect
79. C4×Q8×C11D4semidirect
80. C4×Q8×C11D4semidirect
93. C4×D4×C11D4semidirect
94. C4×D4×C11D4semidirect
128. #32924C11direct (N × H)
217. C4×H(5,𝔽2)C2×C11semidirect
218. #3040C2×C11semidirect
219. C2×#455C2×C11semidirect
221. #2544C2×C11semidirect
222. #1887C2×C11semidirect
223. #1885C2×C11semidirect
224. #1883C2×C11semidirect
225. #1882C2×C11semidirect
226. #1806C2×C11semidirect
227. #1800C2×C11semidirect
297. C2×#124C22×C11semidirect
314. #423C22×C11semidirect
317. #419C22×C11semidirect
318. #418C22×C11semidirect
322. #391C22×C11semidirect
323. #390C22×C11semidirect
325. C4×C4⋊C4C22×C11semidirect
326. #343C22×C11semidirect
327. #339C22×C11semidirect
328. #339C22×C11semidirect
390. C4×Q8D4×C11semidirect
391. C4×Q8D4×C11semidirect
404. C4×D4D4×C11semidirect
405. C4×D4D4×C11semidirect
535. C11#32924direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×C11×H(5,𝔽2)2
C11×#30402
C2×C11×#4552
C2×C11×#4532
C11×#25442
C11×#18872
C11×#18852
C11×#18832
C11×#18822
C11×#18062
C11×#18002
#3292411